Error evaluating the log probability at the initial value (Stan error)

I am trying to run a Vector Autoregression model (VAR (1)) with heteroscedasticity in Stan. I can successfully run the model using JAGS but I don't know why Stan gives some errors when running the same model. Here is the data and model:

library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())

#Simulating data: 
T <- 100
alpha <- 1
gamma_1 <- 1
gamma_2 <- 0.4
sigma <- y <- rep(NA, length = T)
set.seed(123)
sigma[1] <- runif(1)
y[1] <- 0
for (t in 2:T) {
  sigma[t] <- sqrt(gamma_1 + gamma_2 * (y[t - 1] - alpha)^2)
  y[t] <- rnorm(1, mean = alpha, sd = sigma[t])
}

df <- data.frame(y1 = y, y2 = y, x = rnorm(100,0,1))



model_code <- "
data{
  int<lower=1> T;    //Time
  int<lower=2> K;    //location
  matrix[T,K] y;     //Target variable
  vector[T] x;       //Covariate
}
parameters {
  vector[K] alpha;       //Modelling mean: intercept
  real<lower=0> sigma;   //Modelling y: variance
  matrix[K,K] theta;     //AR(1) coefficient matrix
  row_vector[K] mu_t1 ;  //Initial values of the AR process 
  vector[K] beta;        //Covariate's effect coefficient 
}
transformed parameters {
  matrix[T,K] epsilon;   //Residuals (innovation)
  matrix[T,K] mu;        //Mean of the process
  mu[1,] = mu_t1 ;       //Initial values of the time-series
  
  epsilon[1,] = y[1,] - mu[1,];
  
for(k in 1:K){
  for (t in 2:T){
    mu[t,k] =  alpha[k] + theta[k,] * epsilon[t - 1,]' + beta[k] * x[t];
    epsilon[t,k] =  y[t,k] - mu[t,k] ;
    }
  }
 
}
model{
  //priors
for(k in 1:K){  
  alpha[k] ~ normal(0,3);
  beta[k] ~ normal(0,10);
  theta[k,] ~ normal(0,1);
}
mu_t1 ~ normal(7,1) ;
sigma ~ normal(0, 5);

//Model likelihood
for(k in 1:K){
  for (t in 1:T)
    y[t,k] ~ normal(mu[t,k], sigma);
          }
}
"

model_data <- list(
  T = nrow(df), 
  K = 2,
  x = df$x,
  y = df[,1:2]
)


stan_run <- stan(
  data = model_data,
  model_code = model_code
)

When I run this code, Stan stops before starting the sampling saying:

Chain 2: Rejecting initial value: Chain 2: Error evaluating the log probability at the initial value. Chain 2: Exception: normal_lpdf: Location parameter is nan, but must be finite! (in 'model290f30a800bc_9a829e355b070cb7ca3039bdb9dcc780' at line 43)

I am not sure why it can't evaluate the log probability at the initial value. I don't see anything wrong with my inputs. Does anyone know what is going wrong with my code?

I used the print() statement in the transformed parameters block to see which value is Nan (as it's stated in the error). So this is what I did:

"
transformed parameters {
  matrix[T,K] epsilon;   //Residuals (innovation)
  matrix[T,K] mu;        //Mean of the process
  mu[1,] = mu_t1 ;       //Initial values of the time-series
  
  epsilon[1,] = y[1,] - mu[1,];
  
for(k in 1:K){
  for (t in 2:T){
    mu[t,k] =  alpha[k] + theta[k,] * epsilon[t - 1,]' + beta[k] * x[t];
    epsilon[t,k] =  y[t,k] - mu[t,k] ;
    }
  }

print('mu =', mu);
print('epsilon =', epsilon);
print('theta =', theta);
print('beta =', beta);
 
}
"

And parameter mu was the culprit. I find my mistake to be defining the loops incorrectly in the transformed parameters block. The k loop should come after the t loop and replacing them fixes the error and the model runs with no problem.