[PDF] Top 20 On the p th moment estimates for the solution of stochastic differential equations

... The basic existence and uniqueness theorem based on the Picard method of iterations requires the global or, in a weakened version, Lipschitz condition and linear growth con- dition for f and g (see [–]). Then there ... See full document

... | b ( t, x ) − b ( t, y )| ≤ ρ (| x − y |) . (1.5) From the analysis of Section 5, the coefficients of equation (1.3) do not satisfy the global Lip- schitz condition [8] or non-Lipschitz condition [9, 10]. In other ... See full document

... unique solution of quantum stochastic evolution equation driven by an additional operator under the strong topology is achievable using the iterative ...nonclassical stochastic differential ... See full document

... pantograph stochastic differential equations(PSDEs) are special SDDEs that have unbounded delays (see ...the solution for a linear PSDE was established in ...where equations had linear ... See full document

... Stochastic differential equations (SDEs) are well known to model problems from many areas of science and ...of stochastic functional differen- tial equations with infinite delay and its ... See full document

... dx(t) = f (x(t))dt + g(x(t))dB (t), (1.3) where they showed that under the global Lipschitz condition of the coefficients f and g , the EM approximate solution to the SDE (1.2) is exponentially stable in mean ... See full document

... mild solution of equation ...error estimates for the standard Galerkin finite element method with smooth initial ...error estimates for the fully discrete ... See full document

... Summary This thesis examines the asymptotic behaviour of solution flows of 'certain stochastic differential equations utilising the theory of Lyapunov exponents... The approach is taken [r] ... See full document

... ical solution generated by the ...underlying equations by avoiding solving the nontrivial Kolmogorov-Fokker-Planck partial differen- tial ...second moment, but those conditions are still much stronger ... See full document

... integral stochastic averaging ...integral stochastic averaging method is applied to equations of the form ...using stochastic differential ...differential equations (DDEs), by means of ... See full document

... On the one hand, most of the stability criteria concentrate on the exponential stability. In many practical uses, however, stabilizing a system exponentially fast is not economical and sometimes unfeasible. Therefore, it ... See full document

... of stochastic delay differential equations has been widely developed but frequently for the cases where the delay term has a simple ...the solution and then convergence in the mean-square sense is ... See full document

... pth moment of mild solution of impulsive neutral stochastic integro-differential equations driven by fractional Brownian motion and standard Brownian ...mild solution of system (1) by ... See full document

... In the following we will briefly comment on existing literature on the regularity of solutions to stochastic porous media equations. The existence of strong solutions (i.e. | u | m − 1 u ∈ L 2 ((0, T ) ; H ... See full document

... [3] Tagelsir A Ahmed, and Van Casteren, J.A., Precise Estimates for The Solution of Stochastic Functional Differential Equations With Discontinuous Initial Data (Part 1),.Submitted for ... See full document

... a stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) we discuss the uniform boundedness of the pth moment with p > ... See full document

... the stochastic analysis technique and the generalized Halanay inequality, some novel sufficient conditions on pth moment exponential stability of stochastic differential equations with Markovian ... See full document

... Remark 4.4. For the purpose of this remark, we will assume that the initial condition is bounded below. We will again show that one can get the exponential growth by using heat kernel estimates and Proposition ... See full document

... to stochastic function- al differential equations [7] and neutral stochastic functional differential equations [8] to investigate p-th mo- ment exponential ... See full document

... study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type L´ evy pro- ...the solution trajectory of the system is a diffeomorphism as a function ... See full document