I am trying to find out the exponential decay rate of the Probability $Pr(T>n)$ where $T$ is the first hitting time of a gaussian random walk with i.i.d random variables i.e. $S_{n}=\sum_{i=1}^{n}X_{i}$ where $X_{i}$'s are iid and which have non-zero means and are distributed as $\mathcal{N}(m,2m/N)$. The hitting time is respect to a threshold $B$. I can find upper bounds and lower bounds of the above mentioned probability. Does there exist an exact distribution for the same?
2026-03-30 21:11:25.1774905085
Hitting time Distribution of a Gaussian Random Walk
374 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in STOCHASTIC-PROCESSES
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
- Probability being in the same state
- Random variables coincide
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- Why does there exists a random variable $x^n(t,\omega')$ such that $x_{k_r}^n$ converges to it
- Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$
- Why has $\sup_{s \in (0,t)} B_s$ the same distribution as $\sup_{s \in (0,t)} B_s-B_t$ for a Brownian motion $(B_t)_{t \geq 0}$?
- What is the name of the operation where a sequence of RV's form the parameters for the subsequent one?
- Markov property vs. transition function
- Variance of the integral of a stochastic process multiplied by a weighting function
Related Questions in RANDOM-WALK
- Random walk on $\mathbb{Z}^2$
- Density distribution of random walkers in a unit sphere with an absorbing boundary
- Monkey Random walk using binomial distribution
- Find probability function of random walk, stochastic processes
- Random walk with probability $p \neq 1$ of stepping at each $\Delta t$
- Average distance between consecutive points in a one-dimensional auto-correlated sequence
- Return probability random walk
- Random Walk: Quantiles, average and maximal walk
- motion on the surface of a 3-sphere
- Probability of symmetric random walk being in certain interval on nth step
Related Questions in STOPPING-TIMES
- Need to find Conditions to get a (sub-)martingale
- What techniques for proving that a stopping time is finite almost surely?
- Discrete martingale stopping time
- Optional Stopping Theorem for martingales
- Prove that stopped discrete time nonnegative supermartingales are uniformly integrable
- optimal strategy for drawing a deck of cards
- $\frac1n \sum_{i=1}^n W_i(T_i)\to 0$ a.s. for $n\to\infty$
- Brownian Motion Hitting Time of a line with a negative axis intercept
- Random walk with barriers: estimate time since the appearance of a barrier
- Generalizing a proof for the density of stopped subordinators
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?