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1.
Stochastic diferential equations with the time average have received increasing attentions in recent years since they can ofer better explanations for some fnancial models.Since the time average is involved in this class of stochastic diferential equations,in this paper,the linear growth condition and the Lipschitz condition are diferent from the classical conditions.Under the special linear growth condition and the special Lipschitz condition,this paper establishes the existence and uniqueness of the solution.By using the Lyapunov function,this paper also establishes the existence and uniqueness under the local Lipschitz condition and gives the p-th moment estimate.Finally,a scalar example is given to illustrate the applications of our results. 相似文献
2.
In the paper, stochastic differential equations with random impulses and Markovian switching are brought forward, where the
so-called random impulse means that impulse ranges are driven by a series of random variables and impulse times are a random
sequence, so these equations extend stochastic differential equations with jumps and Markovian switching. Then the existence
and uniqueness of solutions to such equations are investigated by employing the Bihari inequality under non-Lipschtiz conditions. 相似文献
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4.
《Stochastic Processes and their Applications》2020,130(4):1879-1896
In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combining the technique of Lyapunov functions with Krylov’s estimate, we also establish exponential ergodicity for the unique strong solution. 相似文献
5.
This paper considers a class of nonlocal stochastic differential equations with time-varying delay whose coefficients are dependent on the pth moment. By applying the fixed point theorem, the existence and uniqueness of the solution of nonlocal stochastic differential delay equations is studied. Also, a class of moment estimates of solutions is considered. The results are a generalization and continuation of the recent results on this issue. An example is provided to illustrate the effectiveness of our results. 相似文献
6.
In this paper we connect the well established theory of stochastic differential inclusions with a new theory of set-valued stochastic differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L2 consisting of square integrable random vectors. We show that for the solution X to a set-valued stochastic differential equation corresponding to a stochastic differential inclusion, there exists a solution x for this inclusion that is a ‖⋅‖L2-continuous selection of X. This result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions, as well as to consider the viability problem for stochastic differential inclusions. 相似文献
7.
In this paper, we study the convergence and stability of the stochastic theta method (STM) for a class of index 1 stochastic delay differential algebraic equations. First, in the case of constrained mesh, i.e., the stepsize is a submultiple of the delay, it is proved that the method is strongly consistent and convergent with order 1/2 in the mean-square sense. Then, the result is further extended to the case of non-constrained mesh where we employ linear interpolation to approximate the delay argument. Later, under a sufficient condition for mean-square stability of the analytical solution, it is proved that, when the stepsizes are sufficiently small, the STM approximations reproduce the stability of the analytical solution. Finally, some numerical experiments are presented to illustrate the theoretical findings. 相似文献
8.
《Indagationes Mathematicae》2023,34(4):820-829
We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between the laws of solutions with different volatility functions. 相似文献
9.
In this paper we obtain some results on the global existence of solution to Itô stochastic impulsive differential equations in M([0,∞),? n ) which denotes the family of ? n -valued stochastic processes x satisfying supt∈[0,∞) \(\mathbb{E}\)|x(t)|2 < ∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results. 相似文献
10.
In this paper, we study the existence and (Hölder) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case , the Hölder exponent (in ) of the local time is , where is the Hurst parameter of the driving fractional Brownian motion. 相似文献
11.
In this paper, we consider scalar linear stochastic differential games with average cost criterions. We solve the dynamic programming equations for these games and give the synthesis of saddle-point and Nash equilibrium solutions.The authors wish to thank A. Ichikawa for providing the initial impetus and helpful advice. 相似文献
12.
For stochastic differential equations with jumps, we prove that W1H transportation inequalities hold for their invariant probability measures and for their process-level laws on the right-continuous path space w.r.t. the L1-metric and uniform metric, under dissipative conditions, via Malliavin calculus. Several applications to concentration inequalities are given. 相似文献
13.
Gh. Constantin 《Journal of Mathematical Analysis and Applications》2004,300(1):12-16
We prove a result on the preservation of the pathwise uniqueness property for the adapted solution to backward stochastic differential equation under perturbations. 相似文献
14.
Bernhard Schmelzer 《International Journal of Approximate Reasoning》2010,51(9):1159-1171
We consider ordinary stochastic differential equations whose coefficients depend on parameters. After giving conditions under which the solution processes continuously depend on the parameters random compact sets are used to model the parameter uncertainty. This leads to continuous set-valued stochastic processes whose properties are investigated. Furthermore, we define analogues of first entrance times for set-valued processes called first entrance and inclusion times. The theoretical concept is applied to a simple example from mechanics. 相似文献
15.
Guangqiang LAN 《Frontiers of Mathematics in China》2013,8(6):1307-1321
We study the large deviation principle of stochastic differential equations with non-Lipschitzian and non-homogeneous coefficients. We consider at first the large deviation principle when the coefficients σ and b are bounded, then we generalize the conclusion to unbounded case by using bounded approximation program. Our results are generalization of S. Fang-T. Zhang's results. 相似文献
16.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):253-259
The paper dealt with generalized stochastic approximation procedures of Robbins-Monro type. We consider these procedures as strong solutions of some stochastic differential equations with respect to semimartingales and investigate their almost sure convergence and mean square convergence 相似文献
17.
Xicheng Zhang 《Journal of Functional Analysis》2007,249(2):454-476
In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space. 相似文献
18.
《Stochastic Processes and their Applications》2014,124(5):1974-2002
In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large. As applications our main results are applied to various types of SPDE such as stochastic reaction–diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier–Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDE. 相似文献
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