J. Rosen

activity

20012024

most citedLate points for random walks in two dimensions

42 citations · 145 across the 45 of their papers we have counts for

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Showing 2009Show all

8 papers · 1 filter

math.PR2009

Large deviations and renormalization for Riesz potentials of stable intersection measures

Xia Chen, Jay Rosen

We study the object formally defined as γ\big([0,t]^{2}\big)=\int\int_{[0,t]^{2}} | X_{s}- X_{r}|^{-σ} dr ds-E\int\int_{[0,t]^{2}} | X_{s}- X_{r}|^{-σ} dr ds, where $X_{t}$ is the…

math.PR2009

An almost sure limit theorem for Wick powers of Gaussian differences quotients

Michael B. Marcus, Jay Rosen

Let G={G(x), x\in R_+}, G(0)=0, be a mean zero Gaussian process with $E (G (x) - G (y))^{2} = σ^{2} (x - y)$ . Let $ρ (x) = \frac{1}{2} \frac{d ^{2}}{d x ^{2}} σ^{2} (x)$ , $x \neq = 0$ . When $ρ^{k}$ is integrable…

math.PR2009

A stochastic calculus proof of the CLT for the L^{2} modulus of continuity of local time

Jay Rosen

We give a stochastic calculus proof of the Central Limit Theorem \[ {\int (L^{x+h}_{t}- L^{x}_{t})^{2} dx- 4ht\over h^{3/2}} \stackrel{\mathcal{L}}{\Longrightarrow}c(\int (L^{x}_{t…

math.PR2009★ 3 cited

Continuous Differentiability of Renormalized Intersection Local Times in R^{1}

Jay S. Rosen

We study $γ_{k} (x_{2}, ..., x_{k}; t)$ , the k-fold renormalized self-intersection local time for Brownian motion in $R^{1}$ . Our main result says that $γ_{k} (x_{2}, ..., x_{k}; t)$ is continuously…

math.PR2009

A CLT for the $L^{2}$ norm of increments of local times of Lévy processes as time goes to infinity

Michael B. Marcus, Jay Rosen

Let $X = {X_{t}, t \in R_{+}}$ be a symmetric Lévy process with local time ${L_{t}^{x}; (x, t) \in R^{1} \times R_{+}^{1}}$ . When the Lévy exponent $ψ(\la)$ is regularly varying at z…

math.PR2009

A CLT for the third integrated moment of Brownian local time increments

Jay Rosen

Let ${L_{t}^{x}; (x, t) \in R^{1} \times R_{+}^{1}}$ denote the local time of Brownian motion. Our main result is to show that for each fixed $t$ $${\int (L^{x+h}_t- L^x_t)^3 dx-12…

Large deviations and renormalization for Riesz potentials of stable intersection measures

An almost sure limit theorem for Wick powers of Gaussian differences quotients

A stochastic calculus proof of the CLT for the L^{2} modulus of continuity of local time

Continuous Differentiability of Renormalized Intersection Local Times in R^{1}

A CLT for the L2 norm of increments of local times of Lévy processes as time goes to infinity

A CLT for the third integrated moment of Brownian local time increments

A CLT for the $L^{2}$ norm of increments of local times of Lévy processes as time goes to infinity