共查询到20条相似文献,搜索用时 15 毫秒
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本文研究一类由分数布朗运动驱动的一维倒向随机微分方程解的存在性与唯一性问题,在假设其生成元满足关于y Lipschitz连续,但关于z一致连续的条件下,通过应用分数布朗运动的Tanaka公式以及拟条件期望在一定条件下满足的单调性质,得到倒向随机微分方程的解的一个不等式估计,应用Gronwall不等式得到了一个关于这类方程的解的存在性与唯一性结果,推广了一些经典结果以及生成元满足一致Lipschitz条件下的由分数布朗运动驱动的倒向随机微分方程解的结果. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):259-277
Systems of Wick stochastic differential equations are studied. Using an estimate on the Wick product we apply Picard iteration to prove a general existence and uniqueness theorem for systems of Wick stochastic differential equations. We also show the solution is stable with respect to perturbations of the noise. This result is used to show that the solution of a linear system of Wick stochastic differential equations driven by smoothed Brownian motion tends to the solution of the corresponding It equation as the smoothed process tends to Brownian motion 相似文献
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Renaud Marty 《Comptes Rendus Mathematique》2004,338(2):167-170
We consider an ordinary differential equation depending on a small parameter and with a long-range random coefficient. We establish that the solution of this ordinary differential equation converges to the solution of a stochastic differential equation driven by a fractional Brownian motion. The index of the fractional Brownian motion depends on the asymptotic behavior of the covariance function of the random coefficient. The proof of the convergence uses the T. Lyons theory of “rough paths”. To cite this article: R. Marty, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
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We consider a measure-valued process that models a self-repelling or self-attracting population. The process is found as the unique solution to an equation driven by historical Brownian motion. The main result is pathwise uniqueness for a historical stochastic differential equation with a singular drift coefficient. 相似文献
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Wolfgang Bock Jos Luís da Silva Ludwig Streit 《Mathematical Methods in the Applied Sciences》2019,42(18):7452-7460
In this paper, we investigate the potential for a class of non‐Gaussian processes so‐called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M‐Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution. 相似文献
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We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate ε in Poissonian obstacles exits from a large domain. Results are formulated in terms of the solution to a semilinear partial
differential equation with singular boundary conditions. The proofs depend on a quenched homogenization theorem for branching
Brownian motion among soft obstacles. 相似文献
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We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation. 相似文献
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We prove a general theorem on the convergence of solutions of stochastic differential equations. As a corollary, we obtain
a result concerning the convergence of solutions of stochastic differential equations with absolutely continuous processes
to a solution of an equation with Brownian motion. 相似文献
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The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations 下载免费PDF全文
In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion. 相似文献
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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation. 相似文献
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E.H. Essaky 《Bulletin des Sciences Mathématiques》2008,132(8):690-710
In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left limits obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem. 相似文献
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We use the stochastic calculus of variations for the fractional Brownian motion to derive formulas for the replicating portfolios for a class of contingent claims in a Bachelier and a Black–Scholes markets modulated by fractional Brownian motion. An example of such a model is the Black–Scholes process whose volatility solves a stochastic differential equation driven by a fractional Brownian motion that may depend on the underlying Brownian motion. 相似文献
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RBSDE''''s with jumps and the related obstacle problems for integral-partial differential equations 总被引:2,自引:0,他引:2
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation. 相似文献
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《Stochastic Processes and their Applications》2002,98(2):289-315
We consider the integral equation driven by a standard Brownian motion and fractional Brownian motion (fBm). Since fBm is not a semimartingale, we cannot use the semimartingale theory to define an integral with respect to the fBm. Furthermore, a well-developed theory of stochastic differential equations is not applicable to solve it. Existence and uniqueness conditions are obtained for a solution in the space of continuous functions with q-bounded variation, q>2. 相似文献
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Fan Yulian 《中国科学A辑(英文版)》2006,49(4):557-573
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional
reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian
framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential
equation. 相似文献
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利用分数布朗运动研究了一种强路径依赖型期权—回望期权的定价问题.首先列出了有关的定义和引理;其次利用该定义和引理建立了分数布朗运动情况下的价格模型,通过鞅方法,得到了回望期权价格所满足的方程;最后分别给出了看跌回望期权和看涨回望期权的定价公式的显式解. 相似文献
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K. Kubilius 《Acta Appl Math》2003,78(1-3):233-242
We consider the integral equation driven by a standard Brownian motion and by a fractional Brownian motion. Sufficient conditions under which the equation has a weak solution are obtained. 相似文献