Chunrong Feng

Two-parameter p, q-variation paths and integrations of local times

In this paper, we prove two main results. The first one is to give a new condition for the existence of two-parameter

Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding

p, q

Pathwise random periodic solutions of stochastic differential equations

-variation path integrals. Our condition of locally bounded

Numerical approximation of random periodic solutions of stochastic differential equations

p,q

On the Borel–Cantelli lemma and its generalization

-variation is more natural and easy to verify than those of Young. This result can be easily generalized to multi-parameter case. The second result is to define the integral of local time

Local Time Rough Path for Lévy Processes

\int_{-\infty}^\infty\int_0^t g(s,x)d_{s,x}L_s(x)

Rough path integral of local time

pathwise and then give generalized It

Some inequalities in functional analysis, combinatorics, and probability theory

\hat {\rm o}

A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals

’s formula when

Anticipating random periodic solutions—I. SDEs with multiplicative linear noise

\nabla^-f(s,x)