Xicheng Zhang

What is he best known for?

The fields of study he is best known for:

• Mathematical analysis
• Hilbert space
• Pure mathematics

Xicheng Zhang mainly focuses on Mathematical analysis, Stochastic differential equation, Stochastic partial differential equation, Applied mathematics and Lipschitz continuity. His Mathematical analysis study combines topics in areas such as Navier–Stokes equations and Pure mathematics. As a member of one scientific family, Xicheng Zhang mostly works in the field of Stochastic differential equation, focusing on Homeomorphism and, on occasion, Well posedness, Differential equation and Diffeomorphism.

He conducts interdisciplinary study in the fields of Stochastic partial differential equation and Type through his works. His work on Martingale as part of general Applied mathematics research is frequently linked to Time reversibility, Markov kernel and Markov renewal process, bridging the gap between disciplines. His Lipschitz continuity research includes themes of Volterra integral equation, Volterra equations and Strong solutions.

His most cited work include:

• Strong solutions of SDES with singular drift and Sobolev diffusion coefficients (74 citations)
• Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients (69 citations)
• Derivative formulas and gradient estimates for SDEs driven by α-stable processes (68 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Mathematical analysis, Stochastic differential equation, Uniqueness, Stochastic partial differential equation and Pure mathematics. His work in Mathematical analysis is not limited to one particular discipline; it also encompasses Navier–Stokes equations. In his research on the topic of Stochastic differential equation, Hölder condition and Heat kernel is strongly related with Bounded function.

His study in Uniqueness is interdisciplinary in nature, drawing from both Invariant measure, Order and Fokker–Planck equation. In his work, First-order partial differential equation is strongly intertwined with Numerical partial differential equations, which is a subfield of Stochastic partial differential equation. His studies in Pure mathematics integrate themes in fields like Hölder's inequality and Classical Wiener space.

He most often published in these fields:

• Mathematical analysis (86.87%)
• Stochastic differential equation (53.12%)
• Uniqueness (36.87%)

What were the highlights of his more recent work (between 2016-2021)?

• Combinatorics (13.13%)
• Bounded function (14.38%)
• Stochastic differential equation (53.12%)

In recent papers he was focusing on the following fields of study:

His scientific interests lie mostly in Combinatorics, Bounded function, Stochastic differential equation, Heat kernel and Semigroup. While the research belongs to areas of Combinatorics, he spends his time largely on the problem of Wiener process, intersecting his research to questions surrounding Navier–Stokes equations and Lebesgue integration. His Bounded function course of study focuses on Uniqueness and Invariant.

His Stochastic differential equation study improves the overall literature in Applied mathematics. His Sobolev space research incorporates themes from Stochastic partial differential equation, Multiplicative function and Irreducibility. His multidisciplinary approach integrates Mathematical analysis and Dissipative system in his work.

Between 2016 and 2021, his most popular works were:

• Heat kernels for time-dependent non-symmetric stable-like operators (34 citations)
• Heat kernels for non-symmetric diffusion operators with jumps (29 citations)
• Ergodicity of stochastic differential equations with jumps and singular coefficients (26 citations)

In his most recent research, the most cited papers focused on:

• Mathematical analysis
• Hilbert space
• Pure mathematics

Xicheng Zhang focuses on Heat kernel, Bounded function, Combinatorics, Stochastic differential equation and Pure mathematics. He studied Heat kernel and Uniqueness that intersect with Martingale, Invariant and Semigroup. His research in Martingale intersects with topics in Wiener process and Mathematical analysis.

His Semigroup research incorporates elements of Stochastic partial differential equation and Sobolev space. His Combinatorics research integrates issues from Well posedness and Lévy process. The Stochastic differential equation study combines topics in areas such as Irreducibility, Multiplicative function, Open problem, Stable process and Singular coefficients.