6 citations · 7 across the 9 of their papers we have counts for
14 papers
Large time behavior of Lévy processes and their nonlocal Schrödinger semigroups
Mateusz Kwaśnicki, Phanuel Mariano, Hugo Panzo +1
We study the large time asymptotics of the Feynman-Kac semigroups of the symmetric Lévy process on unbounded open sets. Our main result proves the exact exponential asymptotic deca…
Survival probability for jump processes in unbounded domains on metric measure spaces
Phanuel Mariano, Jing Wang
We study the large time behavior of the survival probability for symmetric jump processes in unbounded domains with a positive bottom of the spectr…
On a conjecture of a Pólya functional for triangles and rectangles
Rodrigo Bañuelos, Phanuel Mariano
We consider the functional given by the product of the first Dirichlet eigenvalue and the torsional rigidity of planar domains normalized by the area. This scale invariant function…
Spectral bounds for exit times on metric measure Dirichlet spaces and applications
Phanuel Mariano, Jing Wang
Assuming the heat kernel on a doubling Dirichlet metric measure space has a sub-Gaussian bound, we prove an asymptotically sharp spectral upper bound on the survival probability of…
Improved upper bounds for the Hot Spots constant of Lipschitz domains
Phanuel Mariano, Hugo Panzo, Jing Wang
The Hot Spots constant for bounded smooth domains was recently introduced by Steinerberger (2021) as a means to control the global extrema of the first nontrivial eigenfunction of…
CLT with explicit variance for products of random singular matrices related to Hill's equation
Phanuel Mariano, Hugo Panzo
We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill's equation studied by Adams$\unicode{x2013}$Bloch$\unicode{x2…
Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian
Rodrigo Banuelos, Phanuel Mariano, Jing Wang
For domains in , , we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power and the suprem…
Conformal Skorokhod embeddings and related extremal problems
Phanuel Mariano, Hugo Panzo
The conformal Skorokhod embedding problem (CSEP) is a planar variant of the classical problem where the solution is now a simply connected domain whose exit ti…
On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds
Fabrice Baudoin, Maria Gordina, Phanuel Mariano
In this note we show how results in \cite{BaudoinBonnefont2016, BaudoinGarofalo2013, CoulhonJiangKoskelaSikora2017} yield the Cheng-Yau estimate on two classes of sub-Riemannian ma…
Lyapunov exponent and variance in the CLT for products of random matrices related to random Fibonacci sequences
Rajeshwari Majumdar, Phanuel Mariano, Hugo Panzo +2
We consider three matrix models of order 2 with one random entry and the other three entries being deterministic. In the first model, we let $ε\sim\textrm{Bernoulli}\left(\frac…
The financial value of knowing the distribution of stock prices in discrete market models
Ayelet Amiran, Fabrice Baudoin, Skylyn Brock +5
An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utili…
A derivation of the Black-Scholes option pricing model using a central limit theorem argument
Rajeshwari Majumdar, Phanuel Mariano, Lowen Peng +1
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is…
Gradient Bounds for Kolmogorov Type Diffusions
Fabrice Baudoin, Maria Gordina, Phanuel Mariano
We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techn…
Coupling in the Heisenberg group and its applications to gradient estimates
Sayan Banerjee, Maria Gordina, Phanuel Mariano
We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling s…