共查询到20条相似文献,搜索用时 640 毫秒
1.
Martin Becker 《Computational Management Science》2010,7(1):1-17
We introduce a method for generating (Wx,T(m,s),mx,T(m,s),Mx,T(m,s))(W_{x,T}^{(\mu,\sigma)},m_{x,T}^{(\mu,\sigma)},M_{x,T}^{(\mu,\sigma)}) , where Wx,T(m,s)W_{x,T}^{(\mu,\sigma)} denotes the final value of a Brownian motion starting in x with drift μ and volatility σ at some final time T, mx,T(m,s) = inf0 £ t £ TWx,t(m,s)m_{x,T}^{(\mu,\sigma)} = {\rm inf}_{0\leq t \leq T}W_{x,t}^{(\mu,\sigma)} and Mx,T(m,s) = sup0 £ t £ T Wx,t(m,s)M_{x,T}^{(\mu,\sigma)} = {\rm sup}_{0\leq t \leq T} W_{x,t}^{(\mu,\sigma)} . By using the trivariate distribution of (Wx,T(m,s),mx,T(m,s),Mx,T(m,s))(W_{x,T}^{(\mu,\sigma)},m_{x,T}^{(\mu,\sigma)},M_{x,T}^{(\mu,\sigma)}) , we obtain a fast method which is unaffected by the well-known random walk approximation errors. The method is extended
to jump-diffusion models. As sample applications we include Monte Carlo pricing methods for European double barrier knock-out
calls with continuous reset conditions under both models. The proposed methods feature simple importance sampling techniques
for variance reduction. 相似文献
2.
A new generalized Radon transform R
α, β
on the plane for functions even in each variable is defined which has natural connections with the bivariate Hankel transform,
the generalized biaxially symmetric potential operator Δ
α, β
, and the Jacobi polynomials Pk(b, a)(t)P_{k}^{(\beta,\,\alpha)}(t). The transform R
α, β
and its dual Ra, b*R_{\alpha,\,\beta}^{\ast} are studied in a systematic way, and in particular, the generalized Fuglede formula and some inversion formulas for R
α, β
for functions in
La, bp(\mathbbR2+)L_{\alpha,\,\beta}^{p}(\mathbb{R}^{2}_{+}) are obtained in terms of the bivariate Hankel–Riesz potential. Moreover, the transform R
α, β
is used to represent the solutions of the partial differential equations Lu:=?j=1majDa, bju=fLu:=\sum_{j=1}^{m}a_{j}\Delta_{\alpha,\,\beta}^{j}u=f with constant coefficients a
j
and the Cauchy problem for the generalized wave equation associated with the operator Δ
α, β
. Another application is that, by an invariant property of R
α, β
, a new product formula for the Jacobi polynomials of the type Pk(b, a)(s)C2ka+b+1(t)=còòPk(b, a)P_{k}^{(\beta,\,\alpha)}(s)C_{2k}^{\alpha+\beta+1}(t)=c\int\!\!\int P_{k}^{(\beta,\,\alpha)} is obtained. 相似文献
3.
We describe an algorithm for large-scale discrete ill-posed problems, called GKB-FP, which combines the Golub-Kahan bidiagonalization
algorithm with Tikhonov regularization in the generated Krylov subspace, with the regularization parameter for the projected
problem being chosen by the fixed-point method by Bazán (Inverse Probl. 24(3), 2008). The fixed-point method selects as regularization
parameter a fixed-point of the function ‖r
λ
‖2/‖f
λ
‖2, where f
λ
is the regularized solution and r
λ
is the corresponding residual. GKB-FP determines the sought fixed-point by computing a finite sequence of fixed-points of
functions ||rl(k)||2/||fl(k)||2\|r_{\lambda}^{(k)}\|_{2}/\|f_{\lambda}^{(k)}\|_{2}, where fl(k)f_{\lambda}^{(k)} approximates f
λ
in a k-dimensional Krylov subspace and rl(k)r_{\lambda}^{(k)} is the corresponding residual. Based on this and provided the sought fixed-point is reached, we prove that the regularized
solutions fl(k)f_{\lambda}^{(k)} remain unchanged and therefore completely insensitive to the number of iterations. This and the performance of the method when applied to
well-known test problems are illustrated numerically. 相似文献
4.
A class Uk1 (J){\mathcal{U}}_{\kappa 1} (J) of generalized J-inner mvf’s (matrix valued functions) W(λ) which appear as resolvent matrices for bitangential interpolation problems in the generalized Schur class of p ×q mvf¢s Skp ×qp \times q \, {\rm mvf's}\, {\mathcal{S}}_{\kappa}^{p \times q} and some associated reproducing kernel Pontryagin spaces are studied. These spaces are used to describe the range of the
linear fractional transformation TW based on W and applied to Sk2p ×q{\mathcal{S}}_{\kappa 2}^{p \times q}. Factorization formulas for mvf’s W in a subclass U°k1 (J) of Uk1(J){\mathcal{U}^{\circ}_{\kappa 1}} (J)\, {\rm of}\, {\mathcal{U}}_{\kappa 1}(J) found and then used to parametrize the set Sk1+k2p ×q ?TW [ Sk2p ×q ]{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} \cap T_{W} \left[ {\mathcal{S}}_{\kappa 2}^{p \times q} \right]. Applications to bitangential interpolation problems in the class Sk1+k2p ×q{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} will be presented elsewhere. 相似文献
5.
We consider Dirichlet series zg,a(s)=?n=1¥ g(na) e-ln s{\zeta_{g,\alpha}(s)=\sum_{n=1}^\infty g(n\alpha) e^{-\lambda_n s}} for fixed irrational α and periodic functions g. We demonstrate that for Diophantine α and smooth g, the line Re(s) = 0 is a natural boundary in the Taylor series case λ
n
= n, so that the unit circle is the maximal domain of holomorphy for the almost periodic Taylor series ?n=1¥ g(na) zn{\sum_{n=1}^{\infty} g(n\alpha) z^n}. We prove that a Dirichlet series zg,a(s) = ?n=1¥ g(n a)/ns{\zeta_{g,\alpha}(s) = \sum_{n=1}^{\infty} g(n \alpha)/n^s} has an abscissa of convergence σ
0 = 0 if g is odd and real analytic and α is Diophantine. We show that if g is odd and has bounded variation and α is of bounded Diophantine type r, the abscissa of convergence σ
0 satisfies σ
0 ≤ 1 − 1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and α is Diophantine, then the Dirichlet series ζ
g,α
(s) has an analytic continuation to the entire complex plane. 相似文献
6.
Pierre Maréchal 《Optimization Letters》2012,6(2):357-362
We generalize a well known convexity property of the multiplicative potential function. We prove that, given any convex function
g : \mathbbRm ? [0, ¥]{g : \mathbb{R}^m \rightarrow [{0}, {\infty}]}, the function ${({\rm \bf x},{\rm \bf y})\mapsto g({\rm \bf x})^{1+\alpha}{\bf y}^{-{\bf \beta}}, {\bf y}>{\bf 0}}${({\rm \bf x},{\rm \bf y})\mapsto g({\rm \bf x})^{1+\alpha}{\bf y}^{-{\bf \beta}}, {\bf y}>{\bf 0}}, is convex if β ≥ 0 and α ≥ β
1 + ··· + β
n
. We also provide further generalization to functions of the form (x,y1, . . . , yn)? g(x)1+af1(y1)-b1 ···fn(yn)-bn{({\rm \bf x},{\rm \bf y}_1, . . . , {y_n})\mapsto g({\rm \bf x})^{1+\alpha}f_1({\rm \bf y}_1)^{-\beta_1} \cdot \cdot \cdot f_n({\rm \bf y}_n)^{-\beta_n} } with the f
k
concave, positively homogeneous and nonnegative on their domains. 相似文献
7.
Martin Reiris 《Annales Henri Poincare》2010,10(8):1559-1604
Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume ${\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)}Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume
V(k)=(\frac-k3)3Volg(k)(S){\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)} is monotonically decreasing in the expanding direction and bounded below by
Vinf=(\frac-16Y(S))\frac32{\mathcal{V}_{\rm \inf}=\left(\frac{-1}{6}Y(\Sigma)\right)^{\frac{3}{2}}}. Inspired by this fact we define the ground state of the manifold Σ as “the limit” of any sequence of CMC states {(g
i
, K
i
)} satisfying: (i) k
i
= −3, (ii) Viˉ Vinf{\mathcal{V}_{i}\downarrow \mathcal{V}_{\rm inf}}, (iii) Q
0((g
i
, K
i
)) ≤ Λ, where Q
0 is the Bel–Robinson energy and Λ is any arbitrary positive constant. We prove that (as a geometric state) the ground state
is equivalent to the Thurston geometrization of Σ. Ground states classify naturally into three types. We provide examples
for each class, including a new ground state (the Double Cusp) that we analyze in detail. Finally, consider a long time and
cosmologically normalized flow
([(g)\tilde],[(K)\tilde])(s)=((\frac-k3)2g,(\frac-k3)K){(\tilde{g},\tilde{K})(\sigma)=\left(\left(\frac{-k}{3}\right)^{2}g,\left(\frac{-k}{3}\right)K\right)}, where s = -ln(-k) ? [a,¥){\sigma=-\ln (-k)\in [a,\infty)}. We prove that if [(E1)\tilde]=E1(([(g)\tilde],[(K)\tilde])) £ L{\tilde{\mathcal{E}_{1}}=\mathcal{E}_{1}((\tilde{g},\tilde{K}))\leq \Lambda} (where E1=Q0+Q1{\mathcal{E}_{1}=Q_{0}+Q_{1}}, is the sum of the zero and first order Bel–Robinson energies) the flow ([(g)\tilde],[(K)\tilde])(s){(\tilde{g},\tilde{K})(\sigma)} persistently geometrizes the three-manifold Σ and the geometrization is the ground state if Vˉ Vinf{\mathcal{V}\downarrow \mathcal{V}_{\rm inf}}. 相似文献
8.
Tapani Matala-aho 《Constructive Approximation》2011,33(3):289-312
We shall present short proofs for type II (simultaneous) Hermite–Padé approximations of the generalized hypergeometric and
q-hypergeometric series
F(t)=?n=0¥\frac?k=0n-1P(k)?k=0n-1Q(k)tn, Fq(t)=?n=0¥\frac?k=0n-1P(qk)?k=0n-1Q(qk)tn,F(t)=\sum_{n=0}^{\infty}\frac{\prod_{k=0}^{n-1}P(k)}{\prod _{k=0}^{n-1}Q(k)}t^n,\qquad F_q(t)=\sum_{n=0}^{\infty}\frac{\prod_{k=0}^{n-1}P(q^k)}{\prod _{k=0}^{n-1}Q(q^k)}t^n, 相似文献
9.
Dani Szpruch 《The Ramanujan Journal》2011,26(1):45-53
Let
\mathbbF\mathbb{F} be a p-adic field, let χ be a character of
\mathbbF*\mathbb{F}^{*}, let ψ be a character of
\mathbbF\mathbb{F} and let gy-1\gamma_{\psi}^{-1} be the normalized Weil factor associated with a character of second degree. We prove here that one can define a meromorphic
function [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi ,s,\psi) via a similar functional equation to the one used for the definition of the Tate γ-factor replacing the role of the Fourier transform with an integration against y·gy-1\psi\cdot\gamma_{\psi}^{-1}. It turns out that γ and [(g)\tilde]\widetilde{\gamma} have similar integral representations. Furthermore, [(g)\tilde]\widetilde{\gamma} has a relation to Shahidi‘s metaplectic local coefficient which is similar to the relation γ has with (the non-metalpectic) Shahidi‘s local coefficient. Up to an exponential factor, [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi,s,\psi) is equal to the ratio
\fracg(c2,2s,y)g(c,s+\frac12,y)\frac{\gamma(\chi^{2},2s,\psi)}{\gamma(\chi,s+\frac{1}{2},\psi)}. 相似文献
10.
Hassan Issa 《Integral Equations and Operator Theory》2011,70(4):569-582
Let
W ì \mathbb Cd{\Omega \subset{\mathbb C}^{d}} be an irreducible bounded symmetric domain of type (r, a, b) in its Harish–Chandra realization. We study Toeplitz operators Tng{T^{\nu}_{g}} with symbol g acting on the standard weighted Bergman space Hn2{H_\nu^2} over Ω with weight ν. Under some conditions on the weights ν and ν
0 we show that there exists C(ν, ν
0) > 0, such that the Berezin transform [(g)\tilde]n0{\tilde{g}_{\nu_{0}}} of g with respect to H2n0{H^2_{\nu_0}} satisfies:
|