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Walsh’s theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,
Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and
Existence of weak solutions of stochastic wave equations with nonlinearities of a critical growth driven by spatially homogeneous Wiener processes is established in local Sobolev
Stochastic partial differential equations of divergence form with discontinuous and unbounded coefficients are consid- ered in C 1 domains.. Existence and uniqueness results are
Abstract: In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an
Keywords: Brownian motion, random time change, exit boundary, local time, additive func- tional, stochastic differential equation, Khas’minskii’s lemma, spectrally negative
We prove here (by showing convergence of Chen’s series) that linear stochastic differential equa- tions driven by analytic fractional Brownian motion [6, 7] with arbitrary Hurst index
On the other hand, the study of these equations fits nicely into the the larger context of (stochastic) partial differential equations, in particular Hamilton-Jacobi, heat